Most personal computers currently available include simple audio systems to allow users to play music and to provide sound effects for games. These audio systems typically provide poor quality sound, primarily because of the quality of the speakers included in them.
Many stand-alone high fidelity audio systems include a parametric equalizer to allow listeners to compensate for, or alter, the perceived sound quality of their speakers. However, most personal computers do not include parametric equalizers. Even given a personal computer audio system including a parametric equalizer, many users may not be able to improve perceived sound quality because they either do not care to use the equalizer or are unable to determine appropriate equalizer settings.
Thus, a need exists for a personal computer audio system that would automatically improve the perceived sound quality of the speakers without requiring user input, while still accommodating user input. Such a personal audio system should be inexpensive and require no replacement of existing personal computer speakers.
A second-order digital all-pass filter implementation of a parametric audio equalizer is described in: Massie, An Engineering Study of the Four-Multiply Normalized Ladder Filter, Journal of Audio Engineering Society, vol. 7/8, July/August 1993. The transfer function of Massie's four-multiply normalized ladder filter is given by Relationship 1.F(z)=[1+A(z)]/2+G[1−A(z)]/2  (1)                where:        G is the cut/boot parameter; and        and A(z) is described by Relationship 2.A(z)=(z−2+k1(1+k2)z−1+k2)/(1+k1/(1+k2)z−1+k2z−2)  (2)        where:        k1 is the equalizer's first tuning coefficient;        k2 is the equalizer's second tuning coefficient; and        z−1 represents a unit delay.        
The values of the first and second tuning coefficients can be calculated given values for the equalizer parameters: center frequency and bandwidth.k1=−cos(2πFc/Fs)  (3)k2=(1−tan(πFc/(FsQ)))/(1+tan(πFc/(FsQ)  (4)                where:        Fc is center frequency;        Fs is sampling frequency; and        Q is a quality factor given by Fc/Bandwidth.        
FIG. 1 is a signal flow diagram for a four-multiply normalized ladder filter for implementing the parametric equalizer transfer function of Relationship 1. This implementation introduces two filter coefficients, c1 and c2, whose values are defined by Relationships 5 and 6.c1=√{square root over ( )}(1−k12)  (5)c2=√{square root over ( )}(1−k22)  (6)
FIG. 1 also indicates the values at various internal nodes, w1, w2, w3, w4 and w5, within the ladder filter.
Given the signal flow diagram of FIG. 1 and a digital signal processor(DSP), software instructions to implement the four-multiply ladder filter can readily be generated by one of ordinary skill in the art. Massie discloses one set of possible instructions to do so in his paper.
FIG. 2 illustrates the cut and boost spectrums of an implementation of Massie's four-multiply ladder filter. Note that the cut and boost spectrums are not symmetrical; nor are the cut and boost bandwidths identical. The cut bandwidth is approximately 1500 Hz as compared to the boost bandwidth of 2000 Hz. This unexpected spectrum asymmetry during cut and boost is undesirable for audio applications. One reason this asymmetry is undesirable is because it limits the ability of the ladder filter to filter out undesired frequencies, like the higher order harmonics generated by AC power supplies.
Thus, it would be highly desirable to provide a digital audio system with improved audio quality. In particular, it would be highly desirable to provide a digital parametric equalizer with substantially symmetrical cut and boost spectrums.